Washington (CNN) -- A bill to provide medical benefits and compensation for emergency workers who were first on the scene of the September 11, 2001, terror attacks won approval Wednesday from the U.S. House.

The measure passed on a mostly partisan 268-160 vote. The Senate has yet to take up the issue.

President Barack Obama, who supported the measure, hailed its passage.

"It is a critical step for those who continue to bear the physical scars of those attacks," he said in a statement. "I applaud the House for its support of this bill and for standing up on behalf of these heroes, who served our country in its time of greatest need. I look forward to Congress completing consideration of this legislation so I can sign it into law."

"To the living heroes and heroines of 9/11, we have very good news," she said. "Help is on the way. We passed your bill in the House of Representatives."

Fellow New York Democrat Jerrold Nadler said he was "extremely emotional" over the win.

"We won a major victory today, and I am overjoyed," he said. "Today, we put aside a little politics and we did a little right and a little good."

Republicans had complained the $7.4 billion price tag was too high, while Democrats said the government had an obligation to help the first responders to the deadliest terrorism attack in U.S. history. But New York Republican Rep. Peter King was a strong backer of the measure and stood by Maloney and House Speaker Nancy Pelosi as they celebrated the House win.

"What we did was what we had to do," King said, addressing the dozens of first responders who joined the representatives around the podium. "What you did was what you volunteered to do."

"It took a long time, and I'm sorry for that," he said, adding "you can finally get justice after all these years."

Republicans blocked the bill in July after Democrats suspended the rules to stop the minority party from adding unrelated amendments. The move also meant the bill would require a two-thirds majority to pass, and Republicans used it to their advantage, holding the bill to 255 yes votes -- far fewer than the 291 it needed to pass, though far more than it ordinarily would have needed.

Maloney and the other New Yorkers have been working since for a majority vote.

The James Zadroga 9/11 Health Bill -- named after a deceased New York Police Department detective -- seeks to provide free medical coverage for responders and survivors who were exposed to toxins after the attacks.

A coroner linked Zadroga's death in January 2006 to respiratory failure caused by his work in the toxic plume at ground zero. Zadroga was 34.